On selecting the best of two normal populations using a loss function

The problem of selecting the best of two normal populations is considered. In selection problems the usual loss function is the 0-1 one, i.e. the selection goal is to bound, from below, probabilities of making «correct» selections. In the present paper a selection goal based on a general loss function is presented. The two populations have unknown location parameters and «good» populations are the ones with large values of this parameter. The selection rule is given and its performance is investigated. An application is presented. Similar results for the scale parameters of two gamma populations can be found in van der Laan and van Eeden (1996).